spiral 2-6 - usc viterbiee.usc.edu/~redekopp/ee209/slides/ee209spiral2-6.pdf · spiral 2-6...

2-6.1

Spiral 2-6

Semiconductor MaterialMOS Theory

2-6.2

Learning Outcomes

• I understand why a diode conducts current under forward bias but does not under reverse bias

• I understand the three modes of operation of a MOS transistor and the conditions associated with each mode

• I can analyze circuits containing MOS transistors to find current and voltage values by first determining the mode of operation and then applying the appropriate equations

2-6.3

Current, Voltage, & Resistors

• Kirchoff's Current Law

– Sum of current into a node is equal to current coming out of a node

• Kirchoff's Voltage Law

– Sum of voltages around a loop is 0

• Ohm's Law (only applies to resistors or devices that "act" like a resistor)

– I = V/R, R = V/I, or V = IR

– Note: For a resistor, current and voltage are linearly related with R as the slope

2-6.4

DIODES

2-6.5

Semiconductor Material

• Semiconductor material is not a great conductor material in its pure form

– Small amount of free charge

• Can be implanted (“doped”) with other elements (e.g. boron or arsenic) to be more conductive

– Increases the amount of free charge

Pure Silicon P-Type Silicon

(Doped with boron)

Electron acceptors

N-Type Silicon

(Doped with arsenic)

Electron donors

-+

-

+

-+

-

+ - -

-

-

--

-

+

+

-+ ++

+

+

-

+

2-6.6

Transistor Types• Bipolar Junction Transistors (BJT)

– npn or pnp silicon structure

– Small current into very thin base layer controls large currents between emitter and collector

– However the fact that it requires a current into the base means it burns power (P = I*V) and thus limits how many we can integrate on a chip (i.e. density)

• Metal Oxide Semiconductor Field Effect Transistors– nMOS and pMOS MOSFETS

– Voltage applied to insulated gate controls current between source and drain

• Gate input requires no constant current…thus low power!

p-type

+-

-

+

+

n-type p-type

+

++

base collectoremitter

conductive

polysilicon

-

++

+

-

-

-

Gate InputSource Drain

n-type

p-type

npn BJT

N-type MOSFETWe will focus on MOSFET in this class

2-6.7

PN Junction Diode

• Our understanding of how a transistor works will start by analyzing a simpler device: a diode

• A diode can be formed by simply butting up some p-type and n-type material together

p-type n-type

+ VLED -

Anode Cathode

+-

-

--+

+

+

Schematic

symbol of a

diode

Physical

view

2-6.8

The PN Junction

• When we join the two substances the free electrons at the junction will combine with the nearby free holes in a "loose" bond

• This has two effects:– Around the junction there are no more free charges (they've all

combined) creating a depletion region

– Now remember the dopants in n- and p-type material were still neutrally charged (same # of protons/electrons). So this migration has actually created ions and thus an electric field (and thus voltage) in the opposite direction

p-type n-type

+-

-

- -+

+

+

2-6.9

Depletion Region

• Depletion region has no/few free or mobile charge

• A small voltage is induced due to this recombination– N-type material LOST an electron leaving a positive ion

– P-Type material LOST a hole (GAINED an electron) leaving a negative ion

– The voltage is in the opposite direction

Depletion Region

p-type n-type

+-

-

- -+

+

+

+++- - -

n+p-

2-6.10

Forward Bias• Now let's place an external positive voltage source across the diode

– Holes and electrons are pushed toward each other and reduce the depletion region

– If the external voltage is high enough the charges will have enough energy to overcome the gap and start flowing through the diode

– The positive external voltage needed to overcome the depletion region is known as the Threshold Voltage

Depletion Region

p-type n-type

+-

-

- -+

+

+

+++- - -

-+

Human convention of

current as positive

charge flow

Physical reality

of electron flow

VD

2-6.11

Reverse Bias

• Now let's place an external negative voltage source across the diode

– Holes and electrons are attracted to the voltage source terminal (pulled away from the depletion area making the depletion area expand)

– No current is flowing across the junction because both holes and electrons are attracted in opposite directions

Depletion Region

p-type n-type

+

--

-

-+

+

+

+++- - -

- +

-VD

2-6.12

Ideal Diode• A perfect diode would ideally allow current to

flow in one direction only

• It would therefore be a perfect conductor in one direction (forward bias) and a perfect insulator in the other direction (reverse bias)

• Example: Determine the value of ID if a) VA = 5 volts (forward bias) and b) VD = -5 volts (reverse bias)

– Ideal model:

a) ID = VA/RS = 5 V / 50 = 100 mA

b) Diode is in reverse bias and is acting like a perfect insulator, therefore no current can flow and ID = 0

– More realistic:

a) ID = (VA - 0.7v)/RS = 86 mA

b) ID = 0

+

_VA

ID

RS = 50

2-6.13

TRANSISTORS

2-6.14

Carrier Concentration

• Even silicon has some amount of free electrons (n) and holes (p)– We refer to this as the intrinsic carrier concentration

– Note: n = p since a free electron leaves a hole behind

• When we add dopants we change the carrier concentration– NA and ND is the concentration of acceptors and donors respectively

– Note: NA >> p and ND >> n

Pure Silicon P-Type Silicon

(Doped with boron)

Electron acceptors

N-Type Silicon

(Doped with arsenic)

Electron donors

-+

-

+

-+

-

+ - -

-

-

--

-

+

+

-+ ++

+

+

-

+

2-6.15

15

Doped Valence and Conduction Bands

• Impurity atoms, i.e., donors or acceptors replace some silicon atoms in the crystal lattice– Donors: a valence of five e.g., phosphorus (P) or arsenic (As))

– Acceptors: a valence of three, e.g., boron (B))

– Remember these are electrically neutral (same # of protons/electrons), but are easily induced to donate or accept an electron under certain circumstances (i.e. under a voltage)

• If the donors or acceptors get ionized, each donor delivers an electron to the conduction band. Also each acceptor will capture an electron from valence band leaving a hole behind – Normally, at room temperature all donors (density ND) and acceptors

(concentration NA) are ionized

2-6.16

A FEW QUICK NOTES

2-6.17

Body Terminal• Recall a PN junction acts like a diode and allows current flow when Vpn >

Vthresh

• We don't want that current flow so we must always maintain appropriate voltage to keep the "intrinsic" diodes in reverse bias

– Always keep the P-type area at a voltage lower than the N-type

• For NMOS: Keep Body = GND; For PMOS: Keep Body = Vdd– We will often not show the body connection and assume it is appropriately

connected

p-type

Gate Input

Source Input Drain Output

n-type

+

+

+

+

+

+ + + +

+ + +

-

-

-

- - - --

-

-

+

- -- -

n-type

Gate Input

Drain Input

p-type

-

-

-

-

-

- - - -

- - -

-+

+

+

+ + + ++

+

+

-

+ ++ +

NMOSPMOS

Body/Substrate Body/Substrate

Vdd

Source Input

P

N

2-6.18

18

Conventions

• Since the source is always at the lowest voltage (for NMOS) and highest voltage (for PMOS) we generally define all voltages w.r.t. VS

• Conventionally all terminal voltages are defined wrt VS

• We also often draw our schematic symbols w/o showing the body terminal

2-6.19

Source or Drain• Since MOSFETs are symmetric, which terminal is the source

and which is the drain?

• It depends on how we connect it!

• For NMOS: Source is terminal connected to lower voltage

• For PMOS: Source is terminal connected to higher voltage

p-type

Gate Input

Source Input Drain Output

n-type

+

+

+

+

+

+ + + +

+ + +

-

-

-

- - - --

-

-

+

- -- -

n-type

Gate Input

Drain Input

p-type

-

-

-

-

-

- - - -

- - -

-+

+

+

+ + + ++

+

+

-

+ ++ +

NMOS PMOS

Body/Substrate Body/Substrate

Vdd

Source Input

2-6.20

THE BASIC IDEA OF MOS OPERATION

2-6.21

NMOS vs. PMOS

• We will do all our analysis for NMOS but all the analogs hold true for PMOS (same equations but different constants and flipped n/p, etc.)

• Note: There are a LOT of equations we can and will show…

• …HOWEVER we will show you the main equations for the 3 different operating modes of a MOS transistor right now and most of the equations thereafter are just support for those primary ones and do not need to be memorized, etc.

2-6.22

Piece-wise Functions• How would I describe a function that has the

following graph?

– With 3 separate function for the 3 distinct regions of operation

– MOS transistors behave differently for 3 given input conditions, so we will describe those 3 cases with 3 different functions

1 2 3 4 5 6 7 8

4

3

2

1

f(x) = 2, x < 2

x, 2 <= x < 4

-x, 4 <= x <8

2-6.23

NMOS Transistor Physics

• Key idea: MOS operation relies on a voltage being developed in two dimensions

– From gate to source in the x dimension

– From drain to source in the y dimension

p-type

substrate

Gate Input

Source Drain

n-type

+

+

+

+

+

+ + + +

+ + + +

- --

+-

+-

VGS

VDS

x

y

- -- - - --

Body

Connection

2-6.24

MOS Modes of Operation

• Cutoff– Transistor is off (drain to source is open

circuit)

– VGS < VT (Vt is whatever threshold voltage is needed to turn the transitor on…let's say 0.5-1.0V)

• Linear– Transistor is on and drain to source can be

modeled as a resistor

– Linear relationship between voltage/current

• Saturation– Transistor is on and drain to source allows a

fixed amount of current despite increased voltage

2-6.25

NMOS – Cutoff

• If Vgs <= 0, then holes (p) accumulate at the surface preventing a channel from forming

p-type

substrate

Gate Input

Source Drain

n-type

+ + + +

- --

+-

+-

VGS <= 0

VDS

x

y

- -

Body

Connection

+ + ++ + +

+ + + +

2-6.26

NMOS – Depletion

• As Vgs increases but is still below Vt, some electrons are induced into the channel beneath the gate creating a depletion region (still no current can flow) but we are getting closer

p-type

substrate

Gate Input

Source Drain

n-type

+ + + +

- --

+-

+-

0 < VGS < Vt

VDS

x

y

- -

Body

Connection

+ + +

+ + + +

+ + +

2-6.27

NMOS – Inversion

• As Vgs increases and reaches (and increases beyond) VT, enough electrons are induced into the channel

• We assume VDS is still 0 so there is no horizontal field to create a current flow across the channel, but the channel has now formed

p-type

substrate

Gate Input

Source Drain

n-type

+ + + +

- --

+-

+-

VGS > Vt

VDS= 0

x

y

- -

Body

Connection

+ + ++ + + +

+ + +

-- - - - - -Conductive

channel(The voltage all along

the actual channel is

approx. VGS-Vt)

2-6.28

NMOS – Linear Mode• So we have a conductive channel: Vgs > VT

• Now we increase VDS > 0 so current starts to flow

• The more we increase VDS we get a linear increase in the amount of current we can induce to flow

– Wait! If I gave you a black box and showed that current through it grew linearly with voltage across it then…

– …We can treat the black box like a resistor!

p-type

substrate

Gate Input

Source Drain

n-type

+ + + +

- --

+-

+-

VGS > Vt

VDS> 0

x

y

- -

Body

Connection

+ + + +

+ + +

-- - - - - - Conductive

channel-

VD > 0Vs = 0

++

?

+ Vx -

i

ix

Vx

i = mVx

Let m = ___

2-6.29

NMOS – Linear Mode

• What happens as we continue to increase VDS?

• Notice the shape of the channel. It is narrower near the drain? Why?

– Because VD is positive so there is more pull upward on the electrons near the drain than at the source

• As we increase VDS the channel gets more and more narrow near the drain until it actually pinches off.

p-type

substrate

Gate Input

Source Drain

n-type

+ + + +

- --

+-

+-

VGS > Vt

VDS> 0

x

y

- -

Body

Connection

+ + + +

+ + +

-- - - Conductive

channel-

VD > 0Vs = 0

++

2-6.30

30

NMOS – Saturation

In linearregion:

In saturationregion:

Vgs > Vtand0 < Vds < Vgs-Vt(Vds => Ids )

Vgs > VtandVds > Vgs-Vt(Vds => Ids = const)

|Ehor|

> 0

|Ever|

> 0

2-6.31

NMOS – Saturation• Once VDS > (VGS-VT) the channel starts to pinch off

• At this point an increase in VDS (i.e. stronger electric field) doesn't induce more current

– The extra energy being applied is used to simply get the electrons across the depletion zone between the pinched off channel and the drain

– And as we increase VDS the channel pinches off even more meaning we have use more energy to get electrons across

– Analogy: You can carry 15 items from one place to another in 10 minutes. I come to you and say, I'll give you a helper (increase VDS) but you have to transport 30 items (i.e. it becomes more work/harder). Does the rate of transfer change? No, your additional help/energy is wasted on the additional work you have to perform.

p-type

substrate

Gate Input

Source Drain

n-type

+ + + +

- --

+-

+-

VGS > Vt

VDS> 0

x

y

- -

Body

Connection

+ + + +

+ + +

-- - - Conductive

channel-

VD > 0Vs = 0

++

2-6.32

32

Operating in the linear region

Operating at the edge of saturation

Operating beyond saturation

nMOS Cross-sectional View Summary

VDSAT = Voltage where we crossed from linear

(resistive) mode to saturation mode = Voltage

at the pinchoff point =

This is the voltage at which electrons in the

channel are pulled into the drain by Vds rather

than staying at the surface due to Vgs

Any increase in VD beyond VDSAT is dropped across

the depletion region from drain to the pinchoff

point causing the channel to experience the same

voltage VDSAT on one side and thus the same

amount of current to flow through the channel

Another way to think about it:

Vgs > Vgd so the channel is

deeper near the source than the

drain, but a continuous channel

does exist

2-6.33

Summary of MOS Transistor Modes• MOS transistor (Ids/Vds relationship) can

be modeled differently based on different operating conditions– Open circuit (off)

– As a simple resistor between Drain & Source

– As a constant current source between Drain & Source

– Note: 𝐾𝑛 =𝜀𝑜𝑥

𝑡𝑜𝑥𝜇𝑛 (K' = KN for nmos, KP for pmos)

Mode Condition Ids, Vds Relationship

Off 𝑣𝑔𝑠 < 𝑉𝑇 𝐼𝑑𝑠 = 0

Resistive 𝑣𝑔𝑠 > 𝑉𝑇and 𝑣𝑑𝑠 < 𝑣𝑔𝑠 − 𝑉𝑇

𝐼𝑑𝑠 =1

2𝐾′

𝑊

𝐿2 𝑣𝑔𝑠 − 𝑉𝑇 𝑉𝑑𝑠 − 𝑉𝑑𝑠

2

Saturation 𝑣𝑔𝑠 > 𝑉𝑇and 𝑣𝑑𝑠 ≥ 𝑣𝑔𝑠 − 𝑉𝑇

𝐼𝑑𝑠 =1

2𝐾′

𝑊

𝐿𝑣𝑔𝑠 − 𝑉𝑇

2

2-6.34

Getting More Current to Flow• Note: Ids is proportional to K' (KN or KP) AND

the ratio of W/L

• For a transistor 𝐾𝑁 = 𝐶𝑜𝑥𝜇𝑛 =𝜀𝑜𝑥

𝑡𝑜𝑥𝜇𝑛 is some

intrinsic (we can't change it) measurement of how well the transistor we built will conduct…

– [Note: 𝐾𝑃 = 𝐶𝑜𝑥𝜇𝑃 ≠ 𝐾𝑁]

• As a designer we can change W and L

– W = Conductivity ; L = Conductivity

• As circuit designers, we can:– We can easily choose W & L

– Hard to change 𝐾𝑁 or 𝐾𝑃

p-type

Gate InputSource Input Drain Output

n-type

++

++

+ + + +

+ + + +

- - - --

W

L


Resistive 𝑣𝑔𝑠 > 𝑉𝑇and 𝑣𝑑𝑠 < 𝑣𝑔𝑠 − 𝑉𝑇

𝐼𝑑𝑠 =1

2𝐾′

𝑊

𝐿2 𝑣𝑔𝑠 − 𝑉𝑇 𝑉𝑑𝑠 − 𝑉𝑑𝑠

2

Saturation 𝑣𝑔𝑠 > 𝑉𝑇and 𝑣𝑑𝑠 ≥ 𝑣𝑔𝑠 − 𝑉𝑇

𝐼𝑑𝑠 =1

2𝐾′

𝑊

𝐿𝑣𝑔𝑠 − 𝑉𝑇

2

Changing W is something we will do a lot of in digital designs, mainly to

influence delay of a gate

2-6.35

35

nMOS ID as a Function of VDS and VGS

ID vs VGS for VDS > VDSAT

2-6.36

PMOS Operation

• Threshold voltage is now negative (e.g. -0.7V)

– The gate has to be at a low enough voltage compared to the body to repel the electrons and attract free holes to create a conductive channel of holes

n-type

Gate Input

Drain Inputp-type

-

-

-

-

-

- - - -

- - -

-+

+

+

+ + + ++

+

+

-

+ ++ +

PMOS

Body/Substrate

VddSource Input

+-

VG

In linear region:

In saturation region:

Vgs ≤ VtandVgs-Vt < Vds < 0

Vgs ≤ VtandVds < Vgs-Vt

+-

VD

In cutoff:Vgs > Vt

2-6.37

I-V Characteristics• -Vdsp just means the drain is at a lower voltage than the source in

the PMOS

• -Idsp just means the current is actually flowing from source to drain in the PMOS

Vgsn5

Vgsn4

Vgsn3

Vgsn2

Vgsn1

Vgsp5

Vgsp4

Vgsp3

Vgsp2

Vgsp1

VDD

-VDD

Vdsn

-Vdsp

-Idsp

Idsn

0

2-6.38

Summary of NMOS or PMOS Transistors• So that we don't get too caught up in the

negative signs of PMOS transistors let us use the absolute value (ignore direction of current flow and sign of voltage) to arrive at one set of equations for either type

• We assume though:– NMOS: Vgs, Vt, Vds are all non-negative and current flows

from D to S

– PMOS: Vgs, Vt, Vds are all non-positive and current flows from S to D


Off |𝑣𝑔𝑠| <|𝑉𝑇| |𝐼𝑑𝑠| = 0

Resistive 𝑣𝑔𝑠 ≥ |𝑉𝑇| and

𝑣𝑑𝑠 < 𝑣𝑔𝑠 − |𝑉𝑇||𝐼𝑑𝑠| =

1

2𝐾′

𝑊

𝐿2 𝑣𝑔𝑠 − |𝑉𝑇| |𝑉𝑑𝑠| − |𝑉𝑑𝑠|

2

Saturation 𝑣𝑔𝑠 ≥ |𝑉𝑇| and

𝑣𝑑𝑠 ≥ 𝑣𝑔𝑠 − |𝑉𝑇||𝐼𝑑𝑠| =

1

2𝐾′

𝑊

𝐿𝑣𝑔𝑠 − |𝑉𝑇|

2

2-6.39

EXAMPLE DERIVATIONS

2-6.40

40

Example – NMOS Region Calculation

• Vt of an NMOS transistors is 0.35 v

• VDD = 1.2v

• What are the conditions for the transistor to be – ON

• VGS > 0.35

• Assuming Vs = GND, then Vg > 0.35

– In Linear region• VGS > 0.35 and VDS < VGS - 0.35

• In a digital system Vg = 1.2V (logic 1) or 0V (logic 0) so assuming the transistor is on (Vg=1.2V), then VDS < 0.85

– In saturation region• VGS > 0.35 and VDS >= VGS - 0.35

• In a digital system, VDS >= 0.85

Controlling

Input

(Gate)

Output

(Drain )

Source

2-6.41

41

Example – PMOS Region Calculation

• Vt of a PMOS transistors is -0.35 v

• VDD = 1.2v

• What are the conditions for the transistor to be – ON

• VGS < -0.35

• Assuming Vs = Vdd = 1.2V, then Vg < 0.85V

– In Linear region• VGS < -0.35 and VGS – (- 0.35) < VDS < 0

• In a digital system Vg = 1.2V (logic 1) or 0V (logic 0) so assuming the transistor is on (Vg=0V), then - 0.85 < VDS < 0

– In saturation region• VGS < -0.35 and VDS < VGS – (- 0.35)

• In a digital system, VDS < -0.85

Controlling

Input

(Gate)

Source

Output

(Drain)

2-6.42

Example – Current Calculation

• A 0.6 mm process from AMI semiconductor

– tox = 100 angstroms (1 angstrom = 1E-10 m = 1E-8 cm)

– ox =3.9*8.85E-14 F/cm

– m = 350 cm2/V.s

– Vt = 0.7 V

• Plot Ids vs Vds

– Vgs = 0, 1, 2, 3, 4, 5

– Use W/L = 4l/2l

14

2

8

3.9 8.85 10350 120 /

100 10ox

W W WC A V

L L L m m

0 1 2 3 4 50

0.5

1

1.5

2

2.5

Vds

I ds (m

A)

Vgs

= 5

Vgs

= 4

Vgs

= 3

Vgs

= 2

Vgs

= 1

2-6.43

Calculate Vout• Given VT = 0.5, VDD = VGS = 3V, KN = 240 μA/V2, W/L = 1, and RL = 10KΩ

– Note: Vout = VDS and thus VL = VDD-VDS

• Consider what mode the transistor is in, then setup a KCL equation at the output…

– We know VGS-VT is 2.5 while VDS (=Vout) is very likely less-than 2.5 since we have a voltage divider and RL = 10K with most of the 3V dropped across RL leaving Vout to be small

𝐼𝑅𝐿 = 𝐼𝐷𝑆

𝐼𝑅𝐿 =𝑉𝐷𝐷 − 𝑉𝑂𝑈𝑇

𝑅𝐿=1

2𝐾𝑁

𝑊

𝐿2 𝑣𝑔𝑠 − |𝑉𝑇| |𝑉OUT| − |𝑉OUT|

2

3 − 𝑉𝑂𝑈𝑇104

=1

2240 ∗ 10−6 1 2 2.5 |𝑉OUT| − |𝑉OUT|

2


Resistive 𝑣𝑔𝑠 ≥ |𝑉𝑇| and

𝑣𝑑𝑠 < 𝑣𝑔𝑠 − |𝑉𝑇||𝐼𝑑𝑠| =

1

2𝐾′

𝑊

𝐿2 𝑣𝑔𝑠 − |𝑉𝑇| |𝑉𝑑𝑠| − |𝑉𝑑𝑠|

2

Saturation 𝑣𝑔𝑠 ≥ |𝑉𝑇| and

𝑣𝑑𝑠 ≥ 𝑣𝑔𝑠 − |𝑉𝑇||𝐼𝑑𝑠| =

1

2𝐾′

𝑊

𝐿𝑣𝑔𝑠 − |𝑉𝑇|

2

0V

+VDD

IN

OUT

RL

2-6.45

STATIC INVERTER ANALYSISCalculating "DC" (Constant) Voltage Input/Output Relationship

2-6.46

Recall the Inverter• General problem: Given Vin and other

parameters calculate Vout

• Take a moment and think: What should the plot of Vin vs. Vout look like

• How can we calculate Vout, given Vin?

Vout

Vin

= VDS,N

= VDD-

|VDS,P|

= VGS,N

= VDD-

|VGS,P|

Vdd

Vdd

Vout

Vin

= VDS,N

= VDD-

|VDS,P|

= VGS,N

= VDD-

|VGS,P|Ideal (CMOS

comes close)

Other Implementations

may be non-ideal

Vdd

Vin Vout

iSD,P

2-6.47

Step 1: Setup a KCL Equation

• Calculating the static ('steady state') Vin/Vout relationship?

• Use equations for MOS transistors by recognizing the following:– ISD,P = IDS,N + ILOAD according to KCL

– ILOAD = 0 (next gate = no current flow)

– So ISD,P = IDS,N

• The current through the PMOS must equal the current through the NMOS (we can set them equal) and we have equations for the currents (|IDS,P| and |IDS,N|)

Vdd

GND

Vin Vout

Next Gate

(aka “load”)

iSD,P

iDS,N

iLOAD

Vout

Vin

Vdd

Vdd

2-6.48

Step 2: Use Educated Guess for Modes of Operation

• But what mode are they in?– VGS,N = Vin – GND = Vin

– VDS,N = Vout – GND = Vout

– VGS,P = Vin – Vdd and VDS,P = Vdd – Vout

• Given the assumptions…– VT,N = VT,P = 0.5V; Vdd = 3.0V; kn = 2kp;

L=1; Wn = 1; Wp = 2; and Vin = 0.8V

• Then use the Vin/Vout relationship and the given value of Vin to make an educated guess– Since Vin is low, Vout should be "high-ish"

– VGS,N – Vt = 0.3 and VDS,N = "high-ish"• NMOS is in SAT

– |VGS,P|-|VT| = 2.2-0.5 = 1.7V while|VDS,P| = 3V-"high-ish" = small (close to 0)

• PMOS is in LINEAR

Vdd

GND

Vin Vout

Next Gate

(aka “load”)

iSD,P

iDS,N

iLOAD

Vout

Vin

Vdd

Vdd

1. Because Vin = 0.8V…

2 …Vout must be

near Vdd

2-6.49

Step 3: Setup Eqn & Solve for Vout

• Use the current equations for each transistor in its appropriate mode and solve for Vout

𝐼𝑑𝑠,𝑝,𝐿𝐼𝑁 =1

2𝐾𝑃

′ 𝑊

𝐿𝑃

2 𝑣𝑔𝑠,𝑝 − |𝑉𝑇,𝑝| 𝑉𝑑𝑠,𝑝 − 𝑉𝑑𝑠,𝑝2=

|𝐼𝑑𝑠,𝑛,𝑆𝐴𝑇| =1

2𝐾𝑁′

𝑊

𝐿𝑁

𝑣𝑔𝑠,𝑛 − |𝑉𝑇,𝑛|2

1

2𝐾𝑃

′ 𝑊

𝐿 𝑃2 𝑣𝑔𝑠,𝑝 − |𝑉𝑇,𝑝| 𝑉𝑑𝑠,𝑝 − 𝑉𝑑𝑠,𝑝

2=

1

2𝐾𝑁′

𝑊

𝐿 𝑁𝑣𝑔𝑠,𝑛 − |𝑉𝑇,𝑛|

2

1

2𝐾𝑃

′ 2𝑊

𝐿 𝑁2 𝑉𝑑𝑑 − 𝑣𝑖𝑛 − |0.5| 𝑉𝑑𝑑 − 𝑣𝑜𝑢𝑡 − 𝑉𝑑𝑑 − 𝑣𝑜𝑢𝑡

2 = 1

22𝐾𝑃′

𝑊

𝐿 𝑁𝑣𝑖𝑛 − |0.5| 2

2 3 − 0.8 − |0.5| 3 − 𝑣𝑜𝑢𝑡 − 3 − 𝑣𝑜𝑢𝑡2 = 0.8 − |0.5| 2

3.4 ∗ 3 − 𝑣𝑜𝑢𝑡 − 3 − 𝑣𝑜𝑢𝑡2 = 0.09

…continue on to solve for Vout

2-6.50

END LECTURE

2-6.51

51

NMOS – Accumulation

• Vgs ≤ 0

– Actually attracts holes preventing a channel from

forming

2-6.52

52

NMOS – Depletion• For a small positive Vgs, positive holes are repelled creating a

depletion region underneath the gate– The positive gate voltage is still not strong enough to attract enough

free electrons (minority carrier in p-type body) to create a channel

– Note Vds is still 0 (not electric field in the horizontal direction)

|Ehor|

=0

|Ever|

>0

2-6.53

53

NMOS – Inversion

• For a Vgs > some threshold voltage (Vt) a conductive channel is created underneath the gate (the transistor is on)– Now Vgs is large enough to create the inversion layer (a.k.a. channel)

Conductive

channel

|Ehor|

=0

|Ever|

>0

2-6.54

54

NMOS – Modes of Operations

In linear region:

In saturation region:

Vgs > Vtand0 < Vds < Vgs-Vt

Resistive mode (Vds => Ids )

Vgs > VtandVds > Vgs-Vt(Vds => Ids = const) What do you notice about the shape of the channel?

|Ehor|

> 0

|Ever|

> 0

2-6.55

Getting More Current to Flow• Separate random fact: conductivity of material is 𝜎 = 𝑞𝜇𝑛 where 𝜇=mobility and

𝑛 is the concentration of free holes (or electrons depending on material type)

– Note => Conductivity is 1/Resistance

– These are intrinsic properties of the material and the level of doping

• For a transistor 𝐾𝑁 = 𝐶𝑜𝑥𝜇𝑛 =𝜀𝑜𝑥

𝑡𝑜𝑥𝜇𝑛 is some intrinsic measurement of how well

the NMOS transistor structure that we built will conduct…– [Note: 𝐾𝑃 = 𝐶𝑜𝑥𝜇𝑃 ≠ 𝐾𝑁]

• Note that W (Width of channel) and L (Length of channel) also effects conductivity…These are easy for us

– W = Conductivity ; L = Conductivity

• As circuit designers, we can:– We can easily choose W & L

– Hard to change 𝐾𝑁 or 𝐾𝑃

• You'll see us play with W & La lot in digital designs, mainlyto influence delay of a gate

p-type

Gate InputSource Input Drain Output

n-type

++

++

+ + + +

+ + + +

- - - --

W

L

spiral 2-6 - usc viterbiee.usc.edu/~redekopp/ee209/slides/ee209spiral2-6.pdf · spiral 2-6...

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